Home Page Icon
Home Page
Table of Contents for
Title Page
Close
Title Page
by Eung Je Woo, Jin Keun Seo
Nonlinear Inverse Problems in Imaging
Cover
Title Page
Copyright
Preface
List of Abbreviations
Chapter 1: Introduction
1.1 Forward Problem
1.2 Inverse Problem
1.3 Issues in Inverse Problem Solving
1.4 Linear, Nonlinear and Linearized Problems
Reference
Chapter 2: Signal and System as Vectors
2.1 Vector Spaces
2.2 Vector Calculus
2.3 Taylor's Expansion
2.4 Linear System of Equations
2.5 Fourier Transform
References
Chapter 3: Basics of Forward Problem
3.1 Understanding a PDE using Images as Examples
3.2 Heat Equation
3.3 Wave Equation
3.4 Laplace and Poisson Equations
References
Further Reading
Chapter 4: Analysis for Inverse Problem
4.1 Examples of Inverse Problems in Medical Imaging
4.2 Basic Analysis
4.3 Variational Problems
4.4 Tikhonov Regularization and Spectral Analysis
4.5 Basics of Real Analysis
References
Further Reading
Chapter 5: Numerical Methods
5.1 Iterative Method for Nonlinear Problem
5.2 Numerical Computation of One-Dimensional Heat Equation
5.3 Numerical Solution of Linear System of Equations
5.4 Finite Difference Method (FDM)
5.5 Finite Element Method (FEM)
References
Further Reading
Chapter 6: CT, MRI and Image Processing Problems
6.1 X-ray Computed Tomography
6.2 Magnetic Resonance Imaging
6.3 Image Restoration
6.4 Segmentation
References
Further Reading
Chapter 7: Electrical Impedance Tomography
7.1 Introduction
7.2 Measurement Method and Data
7.3 Representation of Physical Phenomena
7.4 Forward Problem and Model
7.5 Uniqueness Theory and Direct Reconstruction Method
7.6 Back-Projection Algorithm
7.7 Sensitivity and Sensitivity Matrix
7.8 Inverse Problem of EIT
7.9 Static Imaging
7.10 Time-Difference Imaging
7.11 Frequency-Difference Imaging
References
Chapter 8: Anomaly Estimation and Layer Potential Techniques
8.1 Harmonic Analysis and Potential Theory
8.2 Anomaly Estimation using EIT
8.3 Anomaly Estimation using Planar Probe
References
Further Reading
Chapter 9: Magnetic Resonance Electrical Impedance Tomography
9.1 Data Collection using MRI
9.2 Forward Problem and Model Construction
9.3 Inverse Problem Formulation using B or J
9.4 Inverse Problem Formulation using Bz
9.5 Image Reconstruction Algorithm
9.6 Validation and Interpretation
9.7 Applications
References
Chapter 10: Magnetic Resonance Elastography
10.1 Representation of Physical Phenomena
10.2 Forward Problem and Model
10.3 Inverse Problem in MRE
10.4 Reconstruction Algorithms
10.5 Technical Issues in MRE
References
Further Reading
Index
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Prev
Previous Chapter
Table of Contents
Next
Next Chapter
Copyright
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset
